Question

Choose the correct option provided below for the following question.
Two angles are supplementary and one angle is twice the other angle then, find both the angles.
A. \[{110^ \circ },{55^ \circ }\]
B. \[{60^ \circ },{120^ \circ }\]
C. \[{70^ \circ },{140^ \circ }\]
D. \[{45^ \circ },{90^ \circ }\]

Answer 1

Hint: We take one angle as a variable and represent another angle in terms of the same variable. We apply the given condition, i.e. twice as the other angle into a linear equation. We solve the equation by using basic mathematics to find the value of one variable. We substitute that in the relation to get another angle as well, hence we get the final solution.

Complete step-by-step solution:
The supplementary angle pair is the pair which when added gives \[{180^ \circ }\].
So, when we add the two angles, if we get \[{180^ \circ }\], the pair of those angles is called supplementary.
Given condition:
One angle is twice the other angle. That means adding these two angles, \[{180^ \circ }\] is obtained.
Let us consider one angle as \[x\].
That means, the other angle is \[2x\].
According to the given condition,
\[x + 2x = 180\]
Adding the terms, we get;
\[3x = 180\]
Rearranging the terms, we get:
\[x = \dfrac{{180}}{3}\]
\[ \Rightarrow x = {60^ \circ }\]
Now that the value of \[x\] is known, we can find the value of \[2x\] by substituting the value of \[x\].
\[ \Rightarrow 2x = 2(60)\]
\[ = {120^ \circ }\]
\[\therefore \] The supplementary angles are \[{60^ \circ },{120^ \circ }\]

The correct option is B.

Note: We can observe that from the solution of the given question, two angles are supplementary when they add up to ${180^ \circ }$. They don’t have to be next to each other, just so long as the total is
${180^ \circ }$. Here, basic mathematics is enough to solve the entire problem. The given condition must be observed carefully and taken into consideration as it is given without getting confused. The application of the supplementary angles, that is having the two angles in a pair of \[{180^ \circ }\] is a proven theorem. You should equate the given condition to the angle rather than equating the condition for itself.